In color image forming apparatuses utilizing electrophotography technology, a tandem-type is the mainstream. In a color image forming apparatus of this type, plural image forming units are disposed in series in order to form a full-color image in a single path. Typically, images formed by the multiple image forming units corresponding to the colors of yellow, magenta, cyan, and black are transferred onto an intermediate transfer belt (intermediate transfer body) for a primary transfer. Then, the multiple images of the various colors on the intermediate transfer belt are transferred onto a recording sheet (recording medium) at once for a secondary transfer, forming an output image thereon. The output image is thereafter fused onto the recording sheet, thus forming a full-color image on the recording medium.
In such a tandem-type image forming apparatus, while improved productivity (number of recording sheets printed per unit time) may be significantly increased, color displacement (registration error) may be caused by positional errors between the various colors on the recording sheet. The positional errors may be caused by positional or size errors of the photosensitive drum in the image forming units or an exposing apparatus, or by an accuracy error of an optical system. Thus, color displacement control (registration control) is indispensable in order to correct such color displacement. In a color displacement control method, a test pattern is formed on the intermediate transfer belt for detecting color displacements among various colors. For example, the position of the test pattern is detected by a sensor, and the amount of color displacement, which may be referred to as a “registration error amount”, is calculated from the detection result. Based on the calculated amount of color displacement, the optical path of various optical systems, image-write starting positions for various colors, or a pixel clock frequency may be corrected.
However, the color displacement control method according to the related art has the following problems.
(1) In order to correct the optical path of an optical system, the corrected optical system which may include a light source and an f-θ lens or mirrors and the like in the optical path need to be mechanically operated in order to align their positions with respect to the various colors. Such an operation requires highly accurate moving components, resulting in an increase in cost. Further, it takes a long time before the correction can be completed, and therefore the correcting operation cannot be performed very frequently.(2) The amount of color displacement (registration error amount) may be changed over time due to deformation of the optical system or supporting members as a result of temperature changes in the apparatus, thus making it difficult to maintain the high image quality that is available immediately after the color displacement control.
In order to solve the problem (1), an image forming apparatus has been proposed whereby a registration error amount is determined based on the coordinates information of test patterns for various colors transferred onto the transfer belt and information about predetermined reference position coordinates of the test patterns. Based on the determined registration error amount, the output coordinates position of image data for each color is automatically converted into a corrected output coordinates position in which the registration error is corrected (see Patent Document 1). In another proposed image forming apparatus, in addition to image position correction with respect to the recording medium in a main scan direction and a sub-scan direction, at least one of image position correction amounts for the recording medium can be changed when forming the registration error detecting pattern and when forming an image. The image position correction amounts may include a magnification ratio and a partial magnification ratio in the main scan direction, a magnification ratio and a partial magnification ratio in the sub-scan direction, lead and side skews, and lead and side linearities (see Patent Document 2).
In order to solve the problem (2), an image forming apparatus is proposed in which the temperature in the apparatus is detected. When there is a certain amount of temperature change, color displacement control is performed. The color displacement control may be repeated after a passage of time.
However, in the technologies according to Patent Documents 1 and 2, although a high-quality image having little color displacement may be formed immediately after color displacement control, it is difficult to maintain the image quality at all times because the color displacement amount is changed over time. The same applies when the color displacement control includes detecting the temperature in the apparatus because the color displacement is not controlled at all times. Further, in the case of the technology involving the temperature detection, the color displacement amount is not directly detected, so that it is difficult to perform color displacement control accurately at appropriate timing in order to keep the displacement amount below a predetermined amount. As a result, the technology may lead to an excess or lack of frequency of color displacement control.
It also takes time to form the color displacement detecting test patterns, detect the test patterns, and calculate the error amount from the detection result. When the test patterns are formed, normal images cannot be printed, and, when the correction involves mechanical control, no printing can be performed until completion of correction when a stable operation can be obtained. Thus, if the color displacement control is performed frequently for maintaining high-quality image formation, productivity decreases.
Further, according to Patent Document 1 or 2, one routine of a color displacement control operation, which is based on information about the temperature changes in the apparatus, the passage of time, or the number of images that are successively formed, includes various processes. The processes include the test pattern formation, the detection of the color displacement amount with reference to the test patterns, and the calculation of the image position correction amount that is used until the next color displacement control based on the detected amount of color displacement. In this case, if a detection error or noise factor is produced in the detected value of color displacement amount, an erroneous image position correction amount is calculated. As a result, an image having color displacement is formed based the erroneous correction amount until the next color displacement control step is performed.
Such detection errors may be reduced by using highly accurate components with increased cost. Alternatively, plural sets of test patterns for color displacement detection may be formed, so that a color displacement amount can be calculated from an average value of multiple sets of detection values. However, in this case, the length of the test patterns may be increased, resulting in an increase in the period in which normal images cannot be printed. Thus, improvements in color displacement correction accuracy may be cancelled by a decrease in productivity.
During a continuous printing operation, the temperature within the apparatus may increase greatly, resulting in large changes in the amount of color displacement and therefore requiring frequent color displacement control. If the color displacement control is performed frequently, the down time in which no printing can be performed due to the test pattern formation and the error amount detection increases, leading to a decrease in productivity. It has been difficult to overcome the aforementioned problems of reduced productivity at the same time.
Namely, variations in color displacement amount may not be found quickly enough due to lack of frequency of color displacement control, or a high-quality image may not be formed due to erroneous correction caused by a detection error or noise. In order to overcome these problems, the frequency of color displacement control may be increased or the length of the test pattern may be increased for improving detection accuracy at the expense of productivity. These problems are particularly felt in printing machines of the electrophotography type, such as digital printing machines, in which high levels are desired for both quality and productivity at all times.
Color displacements in the output image may include not only a linear component that exhibits linear characteristics with respect to a distance in the main scan direction or the sub-scan direction, but also a non-linear component exhibiting non-linear characteristics with respect to such distance. For example, there is a non-linear color displacement referred to as a “scan bow” in the main scan direction as illustrated in FIG. 19(a), which may be caused by an accuracy error in an optical system. Depending on the optical system, a color displacement having curved characteristics with high-order (third-order or higher) components in the main scan direction may be formed, as illustrated in FIG. 19(b). Further, as a non-linear color displacement factor which is mainly caused by an accuracy error in an f-θ lens, a magnification ratio deviation may be caused in which partial magnification ratios of a main-scan magnification ratio of a formed image are varied when the scan speed on the photosensitive drum (image carrier) in the main scan direction is not constant (uniform), resulting in speed deviations on the drum depending on the position in the main scan direction. Such non-linear components of color displacement amounts cannot be corrected by the color displacement control methods according to the related art. Further, some types of color displacement may include a relatively large non-linear component. Thus, improvements in color displacement correction accuracy are desired when applying color displacement control according to the related art to an apparatus having a large non-linear color displacement.    Patent Document 1: Japanese Laid-open Patent Publication No. 8-85236    Patent Document 2: Japanese Laid-open Patent Publication No. 2005-274919